Maxwell equations, curl problem

The differiantial form of faraday's law tells that at a any point in space changing with time magnetic field creates the rotor of electric field (let's say circular electric field at that point), but in the centre of the circular field there is no E vector, it's zero, there only is it's rotor that's not zero, so how can both electric and magnetic fields be created at the same point in space (that tells wave equation solution Esin(wt + kx) and Bsin(wt + kx) if varying one field in time at some point of space there is created only the curl of vector field, but not the vector itself? Meanwhile wave equation solutions' graphs are telling that both electric and magnetic fied exist at the same point in space.